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Lubik-Matthes Natural Rate of Interest

The natural rate of interest is a hypothetical interest rate that is consistent with economic and price stability. There are various estimates of the natural rate in the economics literature, each making certain assumptions about economic interactions. Economists Thomas Lubik at the Richmond Fed and Christian Matthes at Indiana University have devised one such estimate: the Lubik-Matthes Natural Rate of Interest. It is computed using a more flexible economic framework than other popular methods. Their estimate will be updated quarterly.

Latest Reading

The median estimate for the Lubik-Matthes Natural Rate of Interest was −0.3 percent as of the second quarter of 2022.

dates,Lower Bound,Median Estimate,Upper Bound
1-Jan-67,0.789904423,1.613209833,2.424403745
1-Apr-67,0.785964713,1.594741138,2.389501525
1-Jul-67,0.630113341,1.539157716,2.441180197
1-Oct-67,0.564482126,1.519860085,2.47735448
1-Jan-68,0.488900292,1.518600067,2.532315231
1-Apr-68,0.451665346,1.492538011,2.507430922
1-Jul-68,0.535041035,1.473130896,2.397565208
1-Oct-68,0.544145239,1.465597375,2.373348205
1-Jan-69,0.538276325,1.487082725,2.417948895
1-Apr-69,0.380129869,1.418445072,2.419987453
1-Jul-69,0.403421854,1.398279719,2.328282234
1-Oct-69,0.379056806,1.345639803,2.228673317
1-Jan-70,0.429871875,1.349558246,2.192536269
1-Apr-70,0.444366029,1.345692395,2.18046286
1-Jul-70,0.470807673,1.347216583,2.160208728
1-Oct-70,0.324388066,1.280566233,2.135344991
1-Jan-71,0.441739569,1.344819476,2.163917616
1-Apr-71,0.409761461,1.324976508,2.193562642
1-Jul-71,0.456321194,1.361461238,2.214383495
1-Oct-71,0.737304392,1.48751301,2.209735665
1-Jan-72,0.633024031,1.440159712,2.214028673
1-Apr-72,0.543974183,1.412473653,2.257217747
1-Jul-72,0.523099916,1.398680199,2.240009847
1-Oct-72,0.521357727,1.398283859,2.249288053
1-Jan-73,0.364851632,1.337036428,2.244536977
1-Apr-73,-0.143709454,1.087156098,2.181708177
1-Jul-73,-0.529388233,0.92020639,2.157644956
1-Oct-73,-0.324273238,0.947648217,2.041754263
1-Jan-74,-0.572619455,0.791687156,1.923035794
1-Apr-74,-1.634265806,0.335760811,1.846231203
1-Jul-74,-2.028149208,0.140977247,1.742780768
1-Oct-74,-1.044264633,0.530411052,1.779585253
1-Jan-75,-0.366715116,0.874353188,1.878669981
1-Apr-75,-0.045211191,1.009270114,1.934888972
1-Jul-75,-0.119700364,0.941997058,1.963372917
1-Oct-75,-0.182058248,0.908686824,1.948645183
1-Jan-76,-0.129473584,0.936849347,1.96798307
1-Apr-76,-0.044063162,0.991503816,1.980533686
1-Jul-76,-0.283088195,0.891334121,1.953883508
1-Oct-76,-0.251707304,0.912442067,1.989699654
1-Jan-77,-0.196816988,0.984515155,2.112704939
1-Apr-77,0.017000349,1.133632685,2.291539516
1-Jul-77,0.038549652,1.169487092,2.341172779
1-Oct-77,0.126348438,1.23901298,2.40127728
1-Jan-78,0.218085916,1.33262465,2.49298672
1-Apr-78,0.217167929,1.424295395,2.734021979
1-Jul-78,0.242643777,1.454886286,2.776057159
1-Oct-78,0.2362271,1.519556929,2.93582764
1-Jan-79,0.509379532,1.630386381,2.861431612
1-Apr-79,0.263355656,1.586034099,3.030433163
1-Jul-79,0.367290591,1.693416745,3.173195525
1-Oct-79,0.328592773,1.786847495,3.425953833
1-Jan-80,0.256030393,1.811808088,3.531990629
1-Apr-80,0.53058538,1.837390071,3.243515485
1-Jul-80,0.745065981,1.948619567,3.306693695
1-Oct-80,0.75801418,2.32089943,4.200885824
1-Jan-81,1.060275079,2.369236838,4.009884388
1-Apr-81,1.25202486,2.485330101,4.057469366
1-Jul-81,1.382215637,2.54059183,4.033234817
1-Oct-81,1.400861713,2.396527039,3.594350749
1-Jan-82,1.549821429,2.615047089,3.966320666
1-Apr-82,1.685394315,2.70462398,4.022401292
1-Jul-82,1.627263372,2.558056803,3.673546044
1-Oct-82,1.728160827,2.665729616,3.813114624
1-Jan-83,1.856678489,2.785666665,3.969487898
1-Apr-83,1.965039197,2.819667831,3.911221631
1-Jul-83,2.029007852,2.999274591,4.295509229
1-Oct-83,2.064793641,2.961681732,4.155042326
1-Jan-84,2.097661708,2.986530313,4.170180008
1-Apr-84,2.147875365,3.099126214,4.418613976
1-Jul-84,2.129448065,3.028527359,4.257959858
1-Oct-84,2.002755698,2.786640057,3.7422213
1-Jan-85,2.008409367,2.864520636,3.956999553
1-Apr-85,2.011699713,2.827976073,3.841942615
1-Jul-85,2.052176752,2.859818019,3.882761097
1-Oct-85,2.017574198,2.777992737,3.714881507
1-Jan-86,1.946219692,2.721614287,3.648504173
1-Apr-86,1.915975405,2.648327033,3.49361577
1-Jul-86,1.873116368,2.576624294,3.368631426
1-Oct-86,1.914336609,2.645840705,3.502904841
1-Jan-87,1.898959445,2.612785242,3.420896009
1-Apr-87,1.959178694,2.727819306,3.650128582
1-Jul-87,1.914167287,2.684430505,3.588584708
1-Oct-87,1.916569719,2.690388415,3.606567072
1-Jan-88,1.843699786,2.606039014,3.496422325
1-Apr-88,1.864923463,2.67858344,3.630745196
1-Jul-88,1.908755146,2.718514498,3.711995958
1-Oct-88,1.909844894,2.700069896,3.643504429
1-Jan-89,1.92444969,2.702578692,3.647902363
1-Apr-89,1.844536946,2.553961887,3.40786871
1-Jul-89,1.732676864,2.406874801,3.154902913
1-Oct-89,1.597309554,2.281473381,3.02259699
1-Jan-90,1.470061594,2.207889582,2.977068797
1-Apr-90,1.361179165,2.109414681,2.885709676
1-Jul-90,1.246543987,1.99012931,2.733902083
1-Oct-90,1.12761654,1.876287411,2.565285982
1-Jan-91,1.039305671,1.784557959,2.455213442
1-Apr-91,1.171728496,1.878505728,2.543236445
1-Jul-91,1.165793682,1.876540281,2.560270167
1-Oct-91,1.108485529,1.810346233,2.459463698
1-Jan-92,1.125854187,1.805366782,2.444871812
1-Apr-92,1.168374015,1.855325941,2.490215812
1-Jul-92,1.128561742,1.805030706,2.42452606
1-Oct-92,1.146838231,1.829064338,2.474701909
1-Jan-93,1.128638797,1.819043118,2.474531068
1-Apr-93,1.159548252,1.846310265,2.510448187
1-Jul-93,1.256728005,1.918832959,2.566461463
1-Oct-93,1.327964328,1.981347934,2.617944308
1-Jan-94,1.44467199,2.084271926,2.744098916
1-Apr-94,1.574035194,2.237836049,2.979454167
1-Jul-94,1.63111459,2.297825606,3.065589378
1-Oct-94,1.72273951,2.409278973,3.201345624
1-Jan-95,1.734232676,2.427373301,3.239438169
1-Apr-95,1.692015605,2.380544324,3.185514032
1-Jul-95,1.733025173,2.423813937,3.224081632
1-Oct-95,1.732839338,2.440534466,3.237117706
1-Jan-96,1.691656895,2.400103879,3.174033645
1-Apr-96,1.776300456,2.516930743,3.361644152
1-Jul-96,1.790683518,2.561713815,3.428697239
1-Oct-96,1.736828117,2.519363225,3.406076977
1-Jan-97,1.739239903,2.528599128,3.42274761
1-Apr-97,1.809283539,2.642193272,3.615091616
1-Jul-97,1.798707529,2.616876177,3.556508209
1-Oct-97,1.738463679,2.543375404,3.480838798
1-Jan-98,1.776983124,2.596103543,3.595685963
1-Apr-98,1.721003837,2.541571219,3.537466954
1-Jul-98,1.74538552,2.598870265,3.651205382
1-Oct-98,1.515479519,2.327758793,3.225184348
1-Jan-99,1.524555494,2.34032526,3.254425741
1-Apr-99,1.484427823,2.29920095,3.212969895
1-Jul-99,1.538892127,2.391773781,3.381264255
1-Oct-99,1.505154025,2.365980789,3.369880175
1-Jan-00,1.399660045,2.265972302,3.261174917
1-Apr-00,1.488489057,2.395846963,3.461504715
1-Jul-00,1.301996718,2.185698583,3.178535841
1-Oct-00,1.194881503,2.077363041,3.056040771
1-Jan-01,0.874871841,1.732367088,2.574666574
1-Apr-01,0.771124384,1.586273475,2.35747587
1-Jul-01,0.631278266,1.450806082,2.199562402
1-Oct-01,0.309158871,1.215824042,1.977130493
1-Jan-02,0.518897912,1.362044753,2.11971198
1-Apr-02,0.534005957,1.39893484,2.197720246
1-Jul-02,0.424681869,1.301373551,2.0994452
1-Oct-02,0.292571744,1.181005907,1.942885956
1-Jan-03,0.420701394,1.261798568,2.016490586
1-Apr-03,0.455129744,1.284531603,2.042693714
1-Jul-03,0.503187731,1.321941471,2.094643224
1-Oct-03,0.518842252,1.336493875,2.106272784
1-Jan-04,0.389858885,1.234553146,2.027576649
1-Apr-04,0.360762865,1.212690714,2.009895015
1-Jul-04,0.614738538,1.393713726,2.17606054
1-Oct-04,0.687701803,1.480947695,2.28374577
1-Jan-05,0.669339973,1.501070904,2.357003029
1-Apr-05,0.743005895,1.556473496,2.407676437
1-Jul-05,0.876536027,1.688557255,2.551754722
1-Oct-05,0.779097988,1.623389453,2.516201502
1-Jan-06,0.878198784,1.770916179,2.706891238
1-Apr-06,0.784442142,1.712195309,2.701943506
1-Jul-06,0.789457154,1.693557121,2.659046762
1-Oct-06,0.78534866,1.663403401,2.574025916
1-Jan-07,0.677992952,1.607921953,2.561075943
1-Apr-07,0.715516555,1.654733252,2.621399356
1-Jul-07,0.673488048,1.639681533,2.644707736
1-Oct-07,0.318593679,1.305457564,2.230050431
1-Jan-08,-0.29936159,0.730155208,1.594202366
1-Apr-08,-0.329791724,0.702862991,1.56637318
1-Jul-08,-0.440313337,0.639591543,1.55891212
1-Oct-08,-1.249910409,0.056193384,1.030096337
1-Jan-09,-0.683183579,0.447155861,1.360088065
1-Apr-09,-0.563552302,0.550143499,1.470783164
1-Jul-09,-0.480014725,0.60175159,1.514281144
1-Oct-09,-0.52862734,0.604472618,1.575876659
1-Jan-10,-0.794194971,0.328570582,1.274471161
1-Apr-10,-0.77268995,0.32264135,1.261896329
1-Jul-10,-0.606557985,0.438464778,1.359696855
1-Oct-10,-0.761000636,0.332490752,1.285374812
1-Jan-11,-0.855401127,0.295653573,1.29525936
1-Apr-11,-1.015396684,0.166078072,1.208275351
1-Jul-11,-1.122491482,0.051068217,1.06477946
1-Oct-11,-0.987511859,0.113052065,1.085242686
1-Jan-12,-1.188366816,-0.006440649,1.048536174
1-Apr-12,-1.120032682,0.01456966,1.053146248
1-Jul-12,-1.005043581,0.076333104,1.07761457
1-Oct-12,-1.110181646,0.008581009,1.015765222
1-Jan-13,-0.957918936,0.097083368,1.078814726
1-Apr-13,-0.819024914,0.216488523,1.184422104
1-Jul-13,-0.819170304,0.208545288,1.179180442
1-Oct-13,-0.958299037,0.127241078,1.111659734
1-Jan-14,-0.997868813,0.086235665,1.06605863
1-Apr-14,-0.800450931,0.257559491,1.237007606
1-Jul-14,-0.771437016,0.240591923,1.195866556
1-Oct-14,-0.800266705,0.19857823,1.141798648
1-Jan-15,-0.595280266,0.36357242,1.280795963
1-Apr-15,-0.824779873,0.198877063,1.167037856
1-Jul-15,-0.718993707,0.296024824,1.2463732
1-Oct-15,-0.675616849,0.319190007,1.230330108
1-Jan-16,-0.605300816,0.401777338,1.340756383
1-Apr-16,-0.845518191,0.188600977,1.157004487
1-Jul-16,-0.601451889,0.377846847,1.317716769
1-Oct-16,-0.524920494,0.3995455,1.282943484
1-Jan-17,-0.435820328,0.476295742,1.363356545
1-Apr-17,-0.202212078,0.693461403,1.586075681
1-Jul-17,0.008168618,0.897640921,1.791755068
1-Oct-17,-0.052837821,0.857445956,1.761182429
1-Jan-18,-0.097316224,0.857614676,1.804874289
1-Apr-18,-0.042485884,0.924510056,1.905042254
1-Jul-18,0.01528292,0.948745552,1.863380072
1-Oct-18,-0.01886018,0.933334275,1.904080035
1-Jan-19,0.168670775,1.122689535,2.104943108
1-Apr-19,0.04996499,1.081969535,2.110848358
1-Jul-19,0.017336552,1.039241357,2.053041482
1-Oct-19,-0.232675325,0.777944809,1.71950905
1-Jan-20,-0.535352075,0.566622464,1.560117073
1-Apr-20,-1.960362654,-0.242654321,0.99476859
1-Jul-20,-0.073187176,1.127758761,2.345057956
1-Oct-20,-0.287928303,0.829302333,1.903495318
1-Jan-21,-0.680445804,0.577334069,1.710141093
1-Apr-21,-1.624456743,0.190702377,1.71679165
1-Jul-21,-2.286521977,-0.226220281,1.339729093
1-Oct-21,-2.07299886,-0.057362002,1.563643066
1-Jan-22,-3.012406948,-0.523250511,1.255971261
1-Apr-22,-2.602480297,-0.257228519,1.446105869

The real natural rate of interest was computed using the procedure described in Thomas A. Lubik and Christian Matthes, "Calculating the Natural Rate of Interest: A Comparison of Two Alternative Approaches," Federal Reserve Bank of Richmond Economic Brief 15-10, October 2015. Further discussion of this approach based on time-varying parameter VARs can be found in Thomas A. Lubik and Christian Matthes, "Time-Varying Parameter Vector Autoregressions: Specification, Estimation, and an Application," Federal Reserve Bank of Richmond Economic Quarterly, vol. 101, no. 4, Fourth Quarter 2015, pp. 323-352.

What Does the Natural Rate of Interest Mean?

The real natural rate of interest is a key concept for understanding and interpreting macroeconomic relationships and the effects of monetary policy. Interest rates equal to the natural rate are consistent with price and economic stability. Rates above the natural rate slow economic activity and price growth, while rates below the natural rate are stimulative. In other words, it is not the level of the natural rate that matters but its value relative to other interest rates.

The natural rate of interest is thought to be determined by economic fundamentals such as productivity shocks or changes in consumer's preferences. The challenge is that the natural rate of interest is a hypothetical construct that cannot be measured directly. Instead, economists have developed various empirical methods that attempt to derive the natural rate from actual data. The Lubik-Matthes estimate is one such approach that applies fewer theoretical restrictions than other popular methods, such as the Laubach-Williams and Holston-Laubach-Williams models produced at the Federal Reserve Bank of New York.

Additional Resources

Methodology behind the Lubik-Matthes Natural Rate of Interest (non-technical version)

Downloadable data and additional graphs (XLS)

Suggested Citation

Lubik-Matthes Natural Rate of Interest, Federal Reserve Bank of Richmond, last updated September 6, 2022, https://www.richmondfed.org/research/national_economy/natural_rate_interest.